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Triacontahedron [message #57431] Sun, 25 November 2012 16:38 UTC Go to previous message
avatar Magic  is currently offline Magic
Messages: 1293
Registered: August 2008
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Shapie Expert
Shapeways Crew
The Rhombic Triacontahedron is one of my favorite polyhedron.
You can include a dodecahedron and an icosahedron inside it.
I made a model showing those two polyhedra included into a Triacontahedron.
The Triacontahedron is in yellow, the dodecahedron in red and the icosahedron in blue.

The goal of this model is to show how to calculate the volume of the Triacontahedron using those two inclusions. You also need to know that the diagonal (that is the distance bewteen two non consecutive vertices) of a pentagon is the size of its side multiplied by φ, and you need to know how to calculate the volume of a pyramid (one third of the area of its base multiplied by its height).
This video can help.

So can you calculate its volume?

So many things to design, so little time...

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